drummyfish/less_retarded_wiki
5
1
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

Update

Browse source
This commit is contained in:
Miloslav Ciz 2025-05-13 20:44:05 +02:00
parent 1343c90ee8
commit edb70b8898
33 changed files with 2184 additions and 2044 deletions
Download patch file Download diff file Expand all files Collapse all files

2
chess.md
View file

@ -184,7 +184,7 @@ Chess stats are pretty [interesting](interesting.md). Thanks a lot e.g. to OEIS
{ Some chess world records are here: https://timkr.home.xs4all.nl/records/records.htm. ~drummyfish }
**Number of possible games** is not known exactly, Shannon estimated it at 10^120 (lower bound, known as *Shannon number*). Number of possible games by plies played is 20 after 1, 400 after 2, 8902 after 3, 197281 after 4, 4865609 after 5, and 2015099950053364471960 after 15 ([OEIS A048987](https://oeis.org/A048987)).
**Number of possible games** is not known exactly, Shannon estimated it at 10^120 (lower bound, known as *Shannon number*). Number of possible games by plies played is 20 after 1, 400 after 2, 8902 after 3, 197281 after 4, 4865609 after 5, and 2015099950053364471960 after 15 ([OEIS A048987](https://oeis.org/A048987)). { I plotted the ratio of subsequent terms of the sequence and they seem to form a quite predictable pattern, a kind of zig-zag line. I tried to quickly extrapolate this with the curve (5 * x)^0.65 + 17 and estimated the number of games after ply 30 to be 13*10^44. ~drummyfish }
Similarly the **number of possibly reachable positions** (position for which so called *proof game* exists) is not known exactly, some upper estimates have been made, lower bounds are much harder to set. The estimates are placed around 10^40 or 10^50 at most. [Here](https://tromp.github.io/chess/chess.html) is a site that gives a proven upper estimate of 45193640626062205213735739171550309047984050718 (2^155), also providing a more precise one of 7728772977965919677164873487685453137329736522 (~10^45.888, ~2^152) which was however proven with a program that's a bit obscure and less trustworthy. Numbers of possible positions by plies are 20 after 1, 400 after 2, 5362 after 3, 72078 after 4, 822518 after 5, and 726155461002 after 11 ([OEIS A083276](https://oeis.org/A083276)).